Math questionnn? (algebra 1)

"write the standard form of the equation of the line through the pair of points (-2,5) and (-10,10). Write the equation using only integer coefficients"

Yeah, I can find the slope, and put it into point slope formula-- but, I forgot what to do after that D:

An equation for a line is said to be in standard form if it has the form Ax + By = C for some numbers A, B, and C. Here you are asked to make sure that A, B, and C are integers (ie, no fractions are allowed). As you probably have already computed, the slope of this line is (10 - 5)/(-10 - (-2)) = 5/(-8) = -5/8. Using (-2,5) as the point, one way of writing an equation of this line in point slope form is

y - 5 = (-5/8) (x - (-2))

To put this in standard form we just clear the fractions by multiplying both sides by 8, getting 8y - 40 = -5(x + 2), then expand the right hand side, getting 8y - 40 = -5x - 10, and then move all variables to the left hand side and all numbers to the right hand side, getting 5x + 8y = 40 - 10, or

5x + 8y = 30.

This is one answer. There are others (e.g. you could double both sides of the equation, getting 10x + 16y = 60, which is still in standard form, and still represents the same line, and still involves only whole numbers, but since these numbers 10, 16, 60 share a common factor of 2, it is more complicated than the form we originally came up with).